Homework Help

rationalize the denominator: 17x over the fourth root of 9x to the 7th power y to the...

user profile pic

candy1193 | Student, College Freshman | (Level 1) Honors

Posted July 30, 2011 at 10:43 AM via web

dislike 0 like

rationalize the denominator:

17x over the fourth root of 9x to the 7th power y to the sixth power

algebra

1 Answer | Add Yours

user profile pic

shaznl1 | High School Teacher | (Level 1) Salutatorian

Posted July 30, 2011 at 10:54 AM (Answer #1)

dislike 0 like

if your question means 17x/ (4sqrt(9x))^7*y^6), then the procedures will be as follows

times on top and bottom 4sqrt(729x^3)

the fraction becomes

(17x*4sqrt(729x^3))/(4 sqrt(9x*729*x^3)*y^6)

Then the inside of the 4th root becomes 6561 x^4, and the fourth root is just 9 x

put that into the fraction

it becomes (17x*4sqrt(729x^3))/(9x*y^6)

the x cancels on the top side and bottom

it becomes

17*4sqrt(729x^3)/(9*y^6)

If you mean the y^6 is not on the bottom, then just leave it aside and multiply it later

 this question uses that the fourth power of something could cancel out the fourth root, so the fourth power of 9x is 6561x^4 and we had 9x already in the 4th root, so we need to time 729x^3 to the 4th root so that there would be no more radicals on the bottom of the equation, making it rationalized

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes